On the Impacts of Different Consistency Constraint Formulations for Distributed Optimal Power Flow

The optimal power flow (OPF) problem finds the least costly operating point which meets the power grid's operational limits and obeys physical power flow laws. Complementing today's centralized optimization paradigm, future power grids may rely on distributed optimization where multiple agents work together to determine an acceptable operating point. In distributed algorithms, local agents solve subproblems to optimize their region of the system and share data to achieve consistency with their neighboring agents' subproblems. This paper investigates how different methods of enforcing power flow consistency constraints between local areas in distributed optimal power flow impact convergence rate and a classifier's ability to detect malicious cyberattack. The distributed OPF problem is solved with the alternating direction method of multipliers (ADMM) algorithm. First, the ADMM algorithm's convergence rate is compared for three different consistency constraint formulations. Next, the paper considers a cyberattack in which the integrity of information shared between agents is compromised, causing the algorithm to exhibit unacceptable behavior. A support vector machine (SVM) classifier is trained to detect the presence of manipulated data from such cyberattacks. Results demonstrate that consistency constraint formulation impacts the classifier's detection performance; for certain formulations, detection is highly accurate.